# Multiple choice (Probability)

Choose and write the correct option in the following question:(multiple choice of probability )

1.) From the set {1, 2, 3, 4, 5}, two number a and b (a≠ b) are choosen at random. The probability that a/b is an integer is

(a) 1/3                         (b) 1/4

(c) 1/2                          (d) 3/5

2.) A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random (without replacement), then the probability that both the balls are white is

(a) 1/18                        (b) 1/36

(c) 1/12                         (d) 1/24

3.) A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A∪B) = 0.5. Then P(B’∩A) equals

(a) 2/3                          (b) 1/2

(c) 3/10                         (d) 1/5

4.) You are given that A and B are two events such that P(B) = 3/5, P(A|B) = 1/2 and P(A∪B) = 4/5, then P(A) equals

(a) 3/10                        (b) 1/5

(c) 1/2                           (d) 3/5

Answe (c)

5.) Three person, A, B and C fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is

(a) 0.024                    (b) 0.188

(c) 0.336                     (d) 0.452

6.) Assume that in family, each child is equally likely  to be boy or a girl.  A family with three children is choosen random. The probability that the eldest child is a girl given that the family has at least one girl is

(a) 1/2                         (b) 1/3

(c) 2/3                          (d) 4/7

7.) A die is thrown and a card is selected at random from a deck of 52 playing card. The probability of getting an even number on the die and a spade card is

(a) 1/2                           (b) 1/4

(c) 1/8                            (d) 3/4

8.)  A box contains 3 orange balls, 3 green balls and 2 blue ball. Three balls are drawn at random from the box without replacement . The probability of drawing 2 green balls and one blue ball is

(a) 3/28                        (b) 2/21

(c) 1/28                        (d) 167/168

9.) A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is

(a) 33/56                        (b) 9/64

(c) 1/14                             (d) 3/28

10.) Two dice are thrown . If it is known that the sum of number on the dice was less than 6 the probability of getting a sum 3, is

(a) 1/18                            (b) 5/18

(c) 1/5                               (d) 2/5

11.) Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens is

(a) 1/13×1/13                    (b) 1/13×1/12

(c) 1/13×1/17                     (d) 1/13×4/51

12.) A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one ball is red

(a) 15/196                           (b) 131/392

(c) 15/56                              (d) 15/29

13.)  Three persons A, B and C fire at a target in turn, standing with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is

(a) 0.025                              (b) 0.188

(c) 0.339                               (d) 0.475

14.) The probability distribution of a discrete random variable X is given below:

 X 2 3 4 5 P(X) 5/k 7/k 9/k 11/k

The value of k is

(a) 8                                    (b) 16

(c) 32                                   (d) 48

15.) Two dice are thrown together. Let A be the event getting 6 on the first die  and B be the event getting 2 on the

second die then P(A∩B) is

(a) 1/36                           (b) 7/4

(c) 9/20                           (d) None of these

16.) In a college, 30% students fail in physics, 25% fail in Mathematics and 10% fail in both . One student is choosen at random. The probability that she fails in physics if she has failed in mathematics is

(a) 1/10                          (b) 2/5

(c) 9/20                          (d) 1/3

17.) A and B are two students. Their chances of solving a problem correctly are 1/3 and 1/4, respectively. If the probability of their making a common error is, /20 and they obtain the same answer, then the probability of their answer to be correct is

(a) 1/12                          (b) 1/40

(c) 13/120                       (d) 10/13

18.) A mapping is selected at random from set A = {1, 2, 3, …… , 10} into itself. The probability that mapping selected is an injective , is

(a)         (b)

(c)                (d) None of these

19.) If twi events are independent, then

(a) They must be mutually exclusive.

(b) The sum of their probabilities must be equal to 1.

(c) Both (a) and (b) are correct.

(d) None of the above is correct.

20.) If A and B are two events such that P(A) = 1/2, P(B) = 1/3 and P(A/B) = 1/4, then P(A’∩B’) is equal to

(a) 1/12                     (b) 3/4

(c) 1/4                        (d) 3/16